Is there a connection between X11 and gnome?
Yes
Does gnome use the X11 interface for display?
Yes 1
or does gnome perform some of the functions that X11 requires?
Gnome features that users expect / require. X11 does not require Gnome, Gnome requires X11 1 .
X11 is
- a client / server network protocol that allows remote access to displays, keyboards, and mice.
- A low-level API that implements the X11 protocol used to develop graphic applications.
- library (libX11) that implements this API
- a set of packages (servers, toolkits, applications, window managers, etc.) using the X11 API directly and / or using tools.
Gnome -
- a set of applications based on the GTK + suite, which itself uses the X11 API. These applications form a graphical environment that includes many applications, window managers, accessories, ...
There are many other graphical environments, KDE based on the Qt toolkit, which is one of the well-known competitors.
Prior to KDE and Gnome (read in the nineties), one of the most popular desktop systems was CDE, based on the Motif toolkit.
1 Note that you can select alternative base graphics layers with GTK + 3. In this case, you can replace all X11 occurrences in the first part of my answer with the selected backend. Wayland, Quartz, Win32 ...
Relations / dependencies remain unchanged.